刘敏;李订芳;罗一鸣;董建;

• 1:武汉大学数学与统计学院

摘要(Abstract)：

提出一种具有和谐性、保正性和守恒性的非交错中心格式来求解带有干湿面的浅水方程组。根据间断底部的构造定义上、下水位阈值，再基于交错单元的水位值和水位阈值的大小关系判断非交错单元的干湿状态。对干界面和干湿面处的水位值，通过调整相邻单元的水位斜率使其得到修正，保证了格式的和谐性。采用中心龙格库塔方法和构造本质非振荡线性函数使格式在时间和空间方向均具有二阶精度。最后，通过数值算例验证了格式的和谐性、保正性、守恒性和稳健性。

关键词(KeyWords)： 浅水方程组;干湿面;非交错中心格式;和谐格式

Abstract:

Keywords:

基金项目(Foundation): 国家重点基础研究发展计划项目（编号：2017YFC0405901）;; 国家自然科学基金项目（编号：51679143）

作者(Authors): 刘敏;李订芳;罗一鸣;董建;

DOI: 10.14188/j.1671-8844.2023-02-003

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